Particle collision forming Unitarity Triangle

Unlocking the Universe's Secrets: How Scientists Are Using Particle Decays to Measure Fundamental Constants

Soraya Malik in Science & Nature June 2025 • 4 min read.

"Delving into the world of CKM angles and CP violation, a new era of precision measurement is transforming our understanding of the universe."

One of the biggest challenges in particle physics today is accurately determining the fundamental parameters that govern the behavior of matter. Among these, the CKM (Cabibbo-Kobayashi-Maskawa) parameter, specifically the angle 'y', remains one of the least precisely measured angles of the Unitarity Triangle. This angle is crucial for understanding CP violation, a phenomenon where particles and their antiparticles behave differently.

Historically, the best measurements of this angle have come from experiments at B-factories like BaBar and Belle. However, the LHCb experiment at the Large Hadron Collider is poised to take the lead, thanks to its ability to generate a high volume of B meson decays. By studying these decays, scientists can infer the value of 'y' with increasing precision.

At the heart of these measurements are tree-level processes, such as B° → DK+ or B → DK, which are sensitive to the Standard Model interactions. Unlike loop processes that involve more complex quantum corrections, these tree-level decays offer a direct window into the fundamental parameters. Additionally, comparing direct measurements to indirect Standard Model fits can reveal potential tensions, hinting at new physics beyond our current understanding.

Time-Independent Measurements: Decoding CP Violation Through Charged B Decays

Particle collision forming Unitarity Triangle

One primary method for measuring 'y' involves analyzing charged B-hadron decays. This approach focuses on the interference between two types of transitions: b→ u and b→ c within the B→ Dh decay. Here, 'D' represents either a Dº or Dº meson, and 'h' is a K± or π±. The interference is made possible by reconstructing the D meson in a final state that is common to both Dº and Dº. This ensures that the two decay paths, such as B+ → DK+ and B+ → DK+, are indistinguishable.

The sensitivity of this measurement depends significantly on the ratio of the suppressed decay amplitude over the favored B decay amplitude, denoted as rB. The interference also relies on the relative strong phase difference, dB, between the two B amplitudes. To extract 'y', researchers employ three established methods, each tailored to the final state of the D meson:

ADS Method: Utilizes quasi-flavor-specific, doubly Cabibbo-suppressed states (e.g., D → K+π- or D → K+π-π+π-). This method aims for similar decay suppressions (rD) between the interfering B amplitudes, leading to potentially large CP asymmetries.
GLW Method: Employs D mesons that decay into CP eigenstates, which allows for the elimination of D system parameters.
GGSZ Method: Studies three-body self-conjugate D final states (e.g., D → Kπ+π- or D → KK+K-). A Dalitz plot analysis of the D meson decays provides good sensitivity to 'y'.

LHCb has presented results from all three methods, combining various observables from different B decay modes to enhance sensitivity. Direct CP violation in B+ → DK+ has been observed with a total significance of 5.8σ. These combined measurements pave the way for more precise determinations of 'y'.

The Future of CKM Angle Measurements

The ongoing research at LHCb and similar experiments promises to refine our understanding of fundamental constants like the CKM angle 'y'. With updated analyses and increased datasets, the precision of these measurements is set to improve, potentially revealing new insights into the Standard Model and hinting at physics beyond it. The ultimate goal is to reduce the uncertainty in 'y' to approximately 1 degree, using larger datasets and combining various decay channels. This level of precision will allow for stringent tests of the Standard Model and a deeper exploration of CP violation.

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Everything You Need To Know

What is the significance of the CKM angle 'y' in particle physics?

The CKM angle 'y', a parameter within the Cabibbo-Kobayashi-Maskawa matrix, is crucial for understanding CP violation, a phenomenon where particles and their antiparticles behave differently. Accurate measurement of 'y' allows stringent tests of the Standard Model and the exploration of physics beyond it. It's one of the least precisely measured angles of the Unitarity Triangle, making its accurate determination essential for refining our understanding of fundamental constants. More accurate angle y, allows exploration of CP violation implications for matter/antimatter asymmetry. This exploration could provide insights into the universe's composition and evolution, potentially answering why there is more matter than antimatter.

How are scientists measuring the CKM angle 'y', and what are tree-level processes?

Scientists are primarily measuring the CKM angle 'y' by studying B meson decays, especially at the LHCb experiment. They analyze tree-level processes, such as B° → DK+ or B → DK, which provide a direct window into fundamental parameters because they are sensitive to Standard Model interactions without complex quantum corrections. Tree-level processes offer a clearer and less obstructed path to understanding 'y' compared to loop processes, allowing for more precise determination of the CKM angle. Tree level processes are essential for direct measurements because they allow insights in fundamental parameters.

Can you explain the ADS, GLW, and GGSZ methods for measuring 'y' using charged B decays?

The ADS (Atwood-Dunietz-Soni) method uses quasi-flavor-specific, doubly Cabibbo-suppressed states (e.g., D → K+π-). The GLW method employs D mesons that decay into CP eigenstates, eliminating D system parameters. The GGSZ method studies three-body self-conjugate D final states (e.g., D → Kπ+π-), using Dalitz plot analysis of the D meson decays to enhance sensitivity to 'y'. Each method offers a unique way to reconstruct the D meson in a final state common to both Dº and Dº, allowing the extraction of 'y' through the interference between different decay paths. All these methods extract 'y' by focusing on interference and employing different decay characteristics to get to a single value.

How does the LHCb experiment contribute to the measurement of the CKM angle 'y' compared to previous experiments?

The LHCb experiment at the Large Hadron Collider is poised to take the lead in measuring the CKM angle 'y' due to its ability to generate a high volume of B meson decays. Unlike previous experiments at B-factories like BaBar and Belle, LHCb's higher data volume enables scientists to infer the value of 'y' with increasing precision. Additionally, LHCb combines measurements from various observables and B decay modes, enhancing the sensitivity and paving the way for more precise determinations of 'y'. LHCb experiments are allowing the physics community to explore the B meson decays with increased confidence.

What is the ultimate goal in refining the measurement of the CKM angle 'y', and what could be the implications if this goal is achieved?

The ultimate goal is to reduce the uncertainty in the measurement of the CKM angle 'y' to approximately 1 degree. Achieving this level of precision will enable stringent tests of the Standard Model and a deeper exploration of CP violation. Such precision will provide a means for discovering potential tensions between direct measurements and indirect Standard Model fits, possibly hinting at new physics beyond our current understanding. A very precise value allows more accurate Standard model, helping to refine and test the boundaries of the current physics and potential development of the new models.